Problem: Solve for $x$ and $y$ using elimination. ${-3x-3y = -36}$ ${3x+4y = 44}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-3x-3y = -36}\thinspace$ to find $x$ ${-3x - 3}{(8)}{= -36}$ $-3x-24 = -36$ $-3x-24{+24} = -36{+24}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 8}$ into $\thinspace {3x+4y = 44}\thinspace$ and get the same answer for $x$ : ${3x + 4}{(8)}{= 44}$ ${x = 4}$